Optimal. Leaf size=34 \[ -\frac{2 a^2}{\sqrt{x}}+\frac{4}{7} a c x^{7/2}+\frac{2}{15} c^2 x^{15/2} \]
[Out]
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Rubi [A] time = 0.0299939, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 a^2}{\sqrt{x}}+\frac{4}{7} a c x^{7/2}+\frac{2}{15} c^2 x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^2/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 4.49889, size = 32, normalized size = 0.94 \[ - \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**2/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0127433, size = 30, normalized size = 0.88 \[ \frac{2 \left (-105 a^2+30 a c x^4+7 c^2 x^8\right )}{105 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^2/x^(3/2),x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[ -{\frac{-14\,{c}^{2}{x}^{8}-60\,ac{x}^{4}+210\,{a}^{2}}{105}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^2/x^(3/2),x)
[Out]
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Maxima [A] time = 1.43739, size = 32, normalized size = 0.94 \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{7} \, a c x^{\frac{7}{2}} - \frac{2 \, a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226507, size = 35, normalized size = 1.03 \[ \frac{2 \,{\left (7 \, c^{2} x^{8} + 30 \, a c x^{4} - 105 \, a^{2}\right )}}{105 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.7052, size = 32, normalized size = 0.94 \[ - \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**2/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214569, size = 32, normalized size = 0.94 \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{7} \, a c x^{\frac{7}{2}} - \frac{2 \, a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(3/2),x, algorithm="giac")
[Out]